History and Perspective of Quantum Computation

In August 2016, China’s first,
and also the world’s first, quantum communication satellite ‘MoZi’ was
launched. In June 2017, the world’s first experiment on quantum information
across the earth and space – the separation of a pair of entangled photons over
1200km – was realised through the satellite. The first quantum computer was
sold by the Canadian company D-Wave at a price tag of USD10 million in 2011.
Google established its quantum AI lab in 2013. IBM made a 50 quantum-bit cloud
computer in 2017. Over the past decade, the topics of quantum information and
quantum computation have appeared constantly in media; but what do they really
mean? Would we stop using the current computers and switch to quantum computers
in the future?

Probabilistic Algorithm and Parallel Computing

To answer these questions, we
have to begin our story in the last century. With the invention of the
transistor in 1947 and the integrated circuit in the 1950s, the power of
computers greatly increased. Computer scientists made use of the newly acquired
power to solve problems that are beyond the calculation capacity of humans,
such as factoring large integers or encrypting messages by scrambling some
special functions. To reduce computation complexity and thus elevate the
computing speed in these tasks, the scientists proposed what they called
‘probabilistic algorithms’ to compress the computing time from days to minutes
by increasing the parallel concurrence in the algorithms.

In order to appreciate the
difference of probabilistic algorithms from regular algorithms we can consider
a specific example: for example, to find the factors of 14. Besides the trivial
factors 1 and 14, the stupidest way to solve the problem is to try dividing 14
by the numbers 2 up to 7 one-by-one. If it is divisible with a remainder of 0,
then we can determine the relevant number is a factor. Computers are good at
trying one-by-one. Hence, it’s easy to figure out that 2 and 7 are the only two
factors for 14 and these brute-force methods are also easy to program. However,
we would soon realise that the brute-force methods are useful to deal with
integers within 100,000 or 1,000,000 given a powerful computer. If we are to
deal with an integer with, say, 14 digits, we are going to hit a brick wall
since the number of integers we need try dividing is simply too many.

Parallel computing is our
saviour. Suppose we use two computers to try factoring 14, one trying the
factors from 2 to 4 and the other 5 to 7; then the computing time is
instantaneously reduced to half the original. In other words, if the processing
unit of a computer can integrate N computing cores, the computing time
complexity would be reduced to 1/N. Nonetheless, this type of simplification is
still not efficient enough for factoring a very large integer.

Yet, if we are allowed to try
factoring randomly, the efficiency of successfully finding a factor would be
greatly improved, probabilistically speaking. For instance, we have six numbers
2, 3, 4, 5, 6, 7 between 2 and 7. If we do the division of 14 not sequentially
but by picking randomly the candidate factors from these six numbers, it’s
likely that the first one we pick is 7 and the second one 2. In that case, we
don’t even need to try 3, 4, 5, and 6 before we have found all factors of 14.
This is the motivation behind the so-called ‘probabilistic algorithms.’

The Merits of Quantum Computing

Inspired by the concepts of
parallel computing and probabilistic algorithms, Deutsch, C C Yao, and other
computer scientists employed the world view of quantum mechanics – a system can
retain a superposition state to simultaneously coexist on two different
physical settings – in 1980’s to have invented the mathematical model of
quantum Turing machines. In other words, supposing every integer between 2 and
7 can be represented as a physical state, we then only need one quantum system
to form their superposition state and try out the factors in parallel without
increasing the number of computing cores.

Meanwhile, since there is a
probability associated with each state of integer out of the collective
superposition state, these probabilities would increase or decrease
concurrently through the execution of quantum algorithms. The probabilities
associated with the real factors of 14 would gradually approach 1 in
consequence. Therefore, the advantage of quantum computation is that it reduces
the consumption of memory space while alleviating the computing time in
temporal complexity. Shor of Bell Laboratory proposed just such a probabilistic
integer-factoring algorithm geared specifically for quantum computer in 1995.
But so far quantum computation still rests on paper.

After the year 2000, quantum
physicists including Girvin, Martinis, and Tsai successfully fabricated what
they called superconducting quantum-bit (or qubit) systems by carefully
manipulating the Josephson effects on superconducting materials. Thereafter,
the superposition state necessary for quantum computation can be generated in a
solid-state circuit in a controllable fashion. The Martinis group has
implemented Shor’s algorithm to factor the integer 15 using a superconducting
circuit comprising four qubits.

It seems then the making of the
quantum computer has already succeeded and we can make a head start on
commercialising them. But in reality, there is a long road ahead before one can
buy a personal quantum computer. The two most imminent problems are: (i) the
effective data storage time in a qubit is not sufficiently long, being only on
the scale of microseconds; and (ii) the scaling mechanism to share data across
qubits has not yet existed. The latter is also the reason why we can only
factor a small integer like 15 so far. Therefore, one of the current research
directions in our research group at UM is to make use the properties of
solitons on superconducting circuits to prolong the effective storage time,
thus solving the first problem.

But even if the two
aforementioned problems are completely solved, does that mean that the mission
to conquer quantum computation is accomplished? Not quite. Because up to now we
are only using the principles of quantum mechanics to improve the algorithms
for factoring, searching, etc. within the conceptual framework of conventional
computers. Is it possible to employ the postulates of quantum mechanics to
exceed the given structure of Turing machines, making some tasks originally
incomputable computable? About this, we do not yet know the answer.

The author is an associate
professor of the Institute of Applied Physics and Materials Engineering,
University of Macau. He has established the cryogenic quantum computation
laboratory and conducted research studies on quantum optics and quantum
information processing using superconducting circuits. Through his research
experience at the Institute of Theoretical Physics of the Chinese Academy of
Sciences, he has developed an interest in astrophysics, and currently teaches a
general education course on the mysteries of the universe.